how to derive the cross product formula: |u x v| = |u| x |v| sin (angle)

In physics and engineering the work W performed by a constant force F applied in the direction of motion to an object moving a distance d on a straight line is defined to be W = ||F||d(force magnitude times distance) \In the case where the applied force is constant but makes an angle 0 with the direction of motion, and where the object moves along a line from a point P to a point Q, we call PQ the displacement and define the work performed by the force to be W = F • PQ = ||F|||PO||cose (see accompanying figure). Common units of work are ft-Ib (foot-pounds) or Nm (Newton-meters). ||F|| F L||F|| cos 0 -||P|- Work = (1|F|| cos e) ||PQ|| %3D a) Show that the work performed by a constant force (not necessarily in the direction of motion) can be expressed as